Thank you for your kind words!
If the automatic replacement is not working, the the theme search bar must be hard-coded to one of the theme files. I'm guessing you are reffering to the header pop-out search bar.
While customizations and installations are not part of support, I will try to help you with this as much as I can. For this reason I cannot guarantee I'm able to do this.
Can you please add temporary FTP details as well? I will try to track down the theme file that has the search code hard-coded and place it to the child theme directory, and replace it with the plugin shortcode there if possible.
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